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;
; File: Munger.a
;
; Contains: Byte String munger
;
; Copyright: © 1986-1992 by Apple Computer, Inc., all rights reserved.
;
; Change History (most recent first):
;
; <SM3> 10/22/92 CSS Fixed short branch to regular branches.
; <SM2> 5/21/92 kc Append "Trap" to the names of HandToHand, PtrToXHand, PtrToHand,
; HandAndHand and PtrAndHand to avoid name conflict with the glue.
; <6> 2/10/92 JSM Moved this file to Munger folder, keeping all the old revisions.
; <5> 10/17/91 JSM Cleanup header, roll-in FixTypoInFixAtan2 patch from
; MungerPatches.a, remove non-68020 code since we'll never build
; another 68000 ROM, remove 68881 code which was never used.
; <4> 9/28/90 SAM Removed EclipseNOPs that were breaking the 68000 builds.
; <3> 9/13/90 BG Removed <2>. 040s are behaving more reliably now.
; <2> 6/22/90 CCH Added some NOPs for flaky 68040's.
; <C914> 10/29/87 rwh Port to Modern Victorian
; 12/9/86 JTC Back out until state issues resolved.
; <C412> 11/17/86 JTC Add conditional code to implement fixed-pt elems using Ô881.
; <A343> 11/3/86 JTC fixed fixDiv/FracDiv problem. Fixed or frac results with a one
; bit in bit #31 is falsely forced to the overflow value.
; <A279> 10/27/86 JTC Changed two addq instructions to addq.l instructions in Munger.a
; to fix a small rounding problem in the fixed point routines.
; 10/20/86 CRC Added 68020 specific flavors of LongMul, FixMul, FracMul,
; FixRatio
; <C206> 10/9/86 bbm Modified to mpw aincludes.
; <C169> 9/23/86 JTC Replace master ptr bit twiddling with mem mgr calls.
; 2/19/86 BBM Made some modifications to work under MPW
; 8/28/85 BBM Temporarily restored ForRAM Equate
; 7/26/85 RDC Removed ForRAM equate (included in Newequ file)
; 5/13/85 SC Exit bug w/d0 in munger
; 5/8/85 SC Added new trap XMunger
; 5/8/85 SC Fixed bug in 4 May work and cleaned up
; 5/4/85 SC Sped up munger per Ernie suggestions and TextEdit needs. New
; local blockmove proc avoids dispatch for 0-1 bytes moved. Only
; one _SetHandleSize and one less _BlockMove on replace calls
; 4/23/85 JTC Added fixed-point stuff.
; 4/16/85 SC Made HandAndHand more robust, doesn't allow source or dest to
; purge.
; 1/29/85 EHB Added fix to make returned offset correct (=offset + length 2)
; 1/28/85 EHB Added fix to make compare respect string boundaries In
; HandToHand, make original Handle unpurgeable, and if original
; already purged, then don't try to clone it.
; 1/23/85 LAK Adapted for new equate files.
;
MACHINE MC68020
; WARNING: CHANGE HISTORIES APPEAR AT THREE DIFFERENT PLACES IN
; THIS FILE. MAKE SURE YOU CHECK ALL THREE.
; (I know this should be cleaned up, some day it will.)
;---------------------------------------------------------------
; Fixed-point code added 21 Apr 85 by JTC.
; MacApp method code added 08 May 85 by JTC.
; More fixed-point code added 13 May 85 JTC.
;---------------------------------------------------------------
;---------------------------------------------------------------
;
; Byte String munger
;
; FUNCTION Munger( h0: Handle; o0: LONGINT;
; p1: Pointer; l1: LONGINT;
; p2: Pointer; l2: LONGINT ): LONGINT
;
; This routine performs various byte-string manipulations. The general
; theme is that handle "h0" (indirectly pointing to an uninterpereted
; string of bytes) is operated on starting at or beyond byte-offset
; "o0" The pointer/length tuple (p1,l1) defines a substring to
; be replaced with the second substring (p2,l2). There are many
; variations depending on which parameters are nullified by passing
; a zero.
;
; The fully expanded arguments will search h starting at o and replace
; the first occurence of (p1,l1) with (p2,l2).
;
; The variations are:
;
; If p1 = 0 the substring defined by offset "o0" of length "l1" will be
; replaced by the substring (p2,l2). The length parameter l1 can be
; set negative to define substring from o0 to the end of string at H
;
; If l1 = 0 the substring (p2,l2) will simply be inserted at offset "o0"
;
; If p2 = 0 no replacement or deletion will occur; this, with the function
; return value, is useful for locating substrings in h
;
; If l2 = 0 the substring used for replacing is null so a delete will
; occur in all the above cases
;
; The function returned value is the final offset at which the replacement
; occurs. A negative value implies the substring couldn't be found in
; the case of a search. Or was out of range in the case of an offset-type
; specification.
;
;-----------------------------------------------------------------------
BLANKS ON
STRING ASIS
LOAD 'StandardEqu.d'
Bytes PROC EXPORT
EXPORT Munger ; Munger 100% U.S. RDA
EXPORT XMunger ; X-tra Munger <11May85>
; local defs
sloppy EQU -4 ; local copy of slop factor <11May85>
physical EQU sloppy-4 ; physical handle size <11May85>
mungeLink EQU physical ; munger stack frame <11May85>
; parameter defs for both Munger and XMunger <11May85>
h0 EQU 28 ; 4 bytes - Handle
o0 EQU 24 ; 4 bytes - offset
p1 EQU 20 ; 4 bytes - pointer 1
l1 EQU 16 ; 4 bytes - length 1
p2 EQU 12 ; 4 bytes - pointer 2
l2 EQU 8 ; 4 bytes - length 2
return EQU 32 ; 4 bytes - return value
mungeParams EQU 24 ; nBytes of parameters
Munger
LINK A6,#mungeLink ; <11May85>
MOVEM.L D2-D7/A2-A4,-(SP) ; save regs <11May85>
MOVE.L h0(A6),A2 ; get handle <11May85>
MOVE.L A2,A0 ; Get handle size <11May85>
_GetHandleSize
MOVE.L D0,D5 ; save it as logical size <11May85>
MOVE.L D0,physical(A6) ; save it physical too <11May85>
CLR.L sloppy(A6) ; we must be neat <11May85>
BSR.S MungeGuts ; it's the real thing <11May85>
MOVE.L D2,return(A6) ; return offset <11May85>
MOVEQ #mungeParams,D1 ; fix up stack <13May85>
mungeBye
MOVEM.L (SP)+,D2-D7/A2-A4 ; restore regs <11May85>
UNLK A6 ; <11May85>
MOVE.L (SP)+,A0 ; return address <11May85>
ADD D1,SP ; fix up stack <13May85>
JMP (A0) ; <11May85>
; FUNCTION XMunger( slop: LONGINT; h0: Handle; o0: LONGINT; <11May85>
; p1: Pointer; l1: LONGINT; <11May85>
; p2: Pointer; l2: LONGINT ): LONGINT <11May85>
logical EQU 36 ; logical size - LONGINT <11May85>
slop EQU 32 ; slop value - LONGINT <11May85>
xReturn EQU 40 ; 4 bytes - return value <11May85>
xMungeParam EQU 32 ; nBytes of parameters <11May85>
XMunger
LINK A6,#mungeLink ; <11May85>
MOVEM.L D2-D7/A2-A4,-(SP) ; save regs <11May85>
MOVE.L h0(A6),A2 ; get handle <11May85>
MOVE.L A2,A0 ; Get handle size <11May85>
_GetHandleSize
MOVE.L D0,physical(A6) ; save it physical too <11May85>
MOVE.L logical(A6),D5 ; get the logical size <11May85>
MOVE.L slop(A6),sloppy(A6) ; relocate slop value <11May85>
BSR.S MungeGuts ; it's the real thing <11May85>
MOVE.L D2,xReturn(A6) ; return offset <11May85>
MOVEQ #xMungeParam,D1 ; fix up stack <13May85>
BRA mungeBye ; <11May85>
; This is the real munger code, all parameters are off A6 except slop
; Register usage:
;
; A2 contains handle to be munged
; D5 contains handle's size
; D2 contains offset o0 (and modified to contain return value)
; A3 contains pointer one p1
; D3 contains length one l1
; A4 contains pointer two p2
; D4 contains length two l2
MungeGuts
; MOVE.L h0(A6),A2 ; get handle
; MOVE.L A2,A0 ; Get handle size
; _GetHandleSize
; MOVE.L D0,D5 ; save it away
; MOVE.L D0,incisor(A6) ; save it here too
MOVE.L o0(A6),D2 ; get offset
MOVE.L p1(A6),A3 ; get pointer 1
MOVE.L p2(A6),A4 ; get pointer 2
MOVE.L l1(A6),D3 ; get length 1
BEQ doInsert ; if l1 = 0 do insertion only
BPL.S notInfinite ; see if l1 is funny
fixL1
MOVE.L D5,D3 ; l1 = length - o0
SUB.L D2,D3
notInfinite
MOVE.L D5,D0 ; Get length
SUB.L D3,D0 ; length - (delLength+offset)
BLT.S notFound ; escape if search > length
SUB.L D2,D0 ;
BLT.S fixL1 ; it's not ok if negative
MOVE.L A3,D0 ; test for find op (p1 = 0)?
BEQ doDelete ; <SM3> CSS
; Look for substring (p1,l1) starting at "o0"
MOVE.L (A2),D6 ; dereference the handle and save
MOVE.L D5,D7 ; get size of string
SUB.L D3,D7 ; subtract l1 <EHB 28-Jan-84>
ADD.L D6,D7 ; point to last valid search loc
ADD.L D2,D6 ; point to first valid loc(add o0)
outer
MOVE.L D3,D1 ; inner loop ctr for compare
SUBQ.L #1,D1 ; fix up for DBRA <4May85>
MOVE.L D6,A0 ; working copy of handle^
MOVE.L A3,A1 ; working copy of search string
inner
CMP.L D6,D7 ; see if anchor if past limit
BCS.S notFound
CMPM.B (A0)+,(A1)+ ; compare bytes
BNE.S tryNext
; SUBQ.L #1,D1 ; -1 next <4May85>
; BNE.S inner ; <4May85>
DBRA D1,inner ; <4May85>
; If it gets to here, it matched so take the offset and run
MOVE.L D6,D2 ; set offset to anchor loc and..
SUB.L (A2),D2 ; subtract orig. to make into offset
BRA.S tryDelete
; The match failed on this byte, move anchor to next and try again
tryNext
ADDQ.L #1,D6 ; anchor ++
BRA.S outer
; The match failed entirely, go home with negative code
notFound
MOVEQ #-1,D2 ; offset = -1
BRA.S go2Home
; This is a special local version of block move to handle simple cases quickly <4May85>
; that arise from the brain-damaged textedit calls. <4May85>
; <4May85>
bm ; local, faster block move <4May85>
CMP.L A0,A1 ; identity move? <4May85>
BEQ.S zeroErr ; skip if so <4May85>
SUBQ.L #1,D0 ; only move <=1 byte? <4May85>
BLE.S @0 ; small move? <4May85>
ADDQ.L #1,D0 ; fix up subtract above <4May85>
_BlockMoveData ; move 'em on out <4May85
RTS ; adios <4May85>
@0 ; <4May85>
BLT.S zeroErr ; nothing to move <4May85>
MOVE.B (A0),(A1) ; special case 1 byte <4May85>
zeroErr ; <11May85>
MOVEQ #0,D0 ; must return zero <4May85>
RTS ; adios <4May85>
; Special local cover of sethandlesize. Doesn't shrink the handle if newsize <11May85>
; is within sloppy(A6) of physical(A6). And, if it grows it, it adds sloppy(A6)<11May85>
; on for the next time. Since this is called only once per Munger call, it <11May85>
; doesn;t have to update the physical size. <11May85>
; <11May85>
shs ; <11May85>
MOVE.L D0,-(SP) ; save D0 <11May85>
SUB.L physical(A6),D0 ; subtract physical size <11May85>
BEQ.S @0 ; escape if same size <11May85>
BGT.S @1 ; it must be shrinking to check <11May85>
NEG.L D0 ; ABS it <11May85>
CMP.L sloppy(A6),D0 ; within range? <11May85>
BGT.S @1 ; nope, must set away <11May85>
@0 ; <11May85>
ADDQ #4,SP ; drop D0 because we can ignore <11May85>
BRA zeroErr ; the call - return no error <11May85>
@1 ; <11May85>
MOVE.L (SP)+,D0 ; restore D0 <11May85>
ADD.L sloppy(A6),D0 ; add slop value <11May85>
_SetHandleSize ; <11May85>
RTS ; it's been real... <11May85>
; Now delete l1 characters at offset in D2 which contains a possibily modified
; offset "o0"
tryDelete
MOVE.L A4,D0 ; if = 0 no deletion/insertion
BEQ.S go2Home ; just do a find
; Delete the substring at o0 (D2) of length l1(D3)
doDelete
MOVE.L l2(A6),D4 ; get length 2 <4May85>
BNE.S doReplace ; do replace <4May85>
MOVE.L D5,D0 ; calc new size
SUB.L D3,D0 ; = oldsize - l1
MOVE.L D0,D5 ; save new size
SUB.L D2,D0 ; amount to move (length - (o0+l1)
MOVE.L (A2),A1 ; dereference handle for dest.
ADD.L D2,A1 ; and add offset o0
MOVE.L A1,A0 ; source = dest +
ADD.L D3,A0 ; l1
BSR bm ; use our blockmove <4May85>
; _BlockMoveData ; <4May85>
MOVE.L A2,A0 ; reset size
MOVE.L D5,D0 ; new size
BSR shs ; <11May85>
; _SetHandleSize ; <11May85>
go2Home
BRA.S goHome ; done, go home <4May85>
doInsert
MOVE.L l2(A6),D4 ; get length 2
BEQ.S goHome ; if = 0 no insertion go home
MOVE.L D5,D0 ; new size = old + l2
ADD.L D4,D0 ; D5 contains old size
MOVE.L A2,A0 ; get handle
BSR shs ; <11May85>
; _SetHandleSize ; <11May85>
BNE.S goHome ; escape if error
; Make room for new part by sliding over remainder
MOVE.L (A2),A1 ; dereference handle for dest
ADD.L D2,A1 ; offset dest by o0
MOVE.L A1,A0 ; source = dest so far
ADD.L D4,A1 ; offset dest by l2
MOVE.L D5,D0 ; nBytes = oldLength -
SUB.L D2,D0 ; offset -
BSR bm ; use our blockmove <4May85>
; _BlockMove ; <4May85>
finishUp ; <4May85>
MOVE.L (A2),A1 ; dereference handle for dest
ADD.L D2,A1 ; offset dest by o0
MOVE.L A4,A0 ; source = p2
MOVE.L D4,D0 ; nBytes = l2
BSR bm ; use our blockmove <4May85>
; _BlockMove ; <4May85>
ADD.L D4,D2 ; return offset + length 2 <EHB 29-Jan-85>
goHome
RTS ; <11May85>
; Replace the substring at o0(D2) of length l1(D3) with substring at <8May85>
; p2(A4) of length l2(D4). Thanks Ernie... <8May85>
; Decide whether the thing is growing or shrinking. If growing, the handle <8May85>
; handlesize is set 1st, then the trailing piece moved. If shrinking, the <8May85>
; piece is moved first, the handleSize set. After that, the new piece is <8May85>
; inserted <8May85>
; <8May85>
doReplace ; <8May85>
MOVE.L D4,D1 ; start with l2 <8May85>
SUB.L D3,D1 ; subtract l1 <8May85>
BEQ.S finishUp ; skip if no change <8May85>
BGT.S @0 ; handle's growing, bm after <8May85>
; <8May85>
BSR.S MoveTail ; move the tail <8May85>
@0 ; <8May85>
MOVE.L A2,A0 ; get handle <8May85>
MOVE.L D5,D0 ; get old size <8May85>
ADD.L D1,D0 ; add delta l2-l1 <8May85>
; <8May85>
BSR shs ; <11May85>
; _SetHandleSize ; <11May85>
BNE goHome ; oops <8May85>
; <8May85>
; Now slide the trailing piece up to make room for insertion <8May85>
; <8May85>
TST.L D1 ; did handle grow? <8May85>
BMI finishUp ; if so, block move done before <8May85>
; <8May85>
BSR.S MoveTail ; move the tail <8May85>
; <8May85>
BRA finishUp ; go finish up <8May85>
MoveTail ; <8May85>
MOVE.L (A2),A1 ; dereference handle for dest. <8May85>
ADD.L D2,A1 ; and add offset o0 <8May85>
; <8May85>
MOVE.L A1,A0 ; source = dest + <8May85>
ADD.L D3,A0 ; l1 <8May85>
ADD.L D4,A1 ; add offset o0 and length l2 <8May85>
; <8May85>
MOVE.L D5,D0 ; get old size <8May85>
SUB.L D3,D0 ; = oldsize - l1 <8May85>
SUB.L D2,D0 ; amt to move (length - (o0+l1) <8May85>
; <8May85>
BRA bm ; use our blockmove <8May85>
;----------------------------------------------------------------------
;
; Handle /Pointer clone routines
;
;
; HandToHand takes a handle in A0 and returns a clone in A0
; PtrToXHand takes a pointer in A0, a handle in A1, and a size in D0. It
; clones the pointer from A0 into the existing handle in A1
; PtrToHand takes a pointer in A0, a size in D0 and returns a clone in A0
; HandAndHand takes handle in A0 and concatenates to handle in A1
; PtrAndHand takes ptr,length in A0,D0 and concatenates to handle in A1
;
; Returns Memory Mgr code in D0
;
EXPORT HandToHandTrap
EXPORT PtrToXHandTrap
EXPORT PtrToHandTrap
EXPORT HandAndHandTrap
EXPORT PtrAndHandTrap
HandToHandTrap
_HGetState ; D0 <- master ptr state<C169>
MOVE.B D0,-(SP) ; save for exit <C169>
MOVE.L A0,-(SP) ; save the handle <EHB 28-Jan-85>
_HNoPurge ; nonpurgeable for now <C169>
MOVE.L A0,A1 ; save the handle <EHB 28-Jan-85>
_GetHandleSize ; and get the size <EHB 28-Jan-85>
TST.L D0 ; purged handle? <EHB 28-Jan-85>
BMI.S handRest ; =>yes, exit pronto <EHB 28-Jan-85>
MOVE.L D0,D1 ; save length <EHB 28-Jan-85>
_NewHandle ; <EHB 28-Jan-85>
MOVE.L (A1),A1 ; dereference source into A1 <EHB 28-Jan-85>
BSR.S cloneCommon ; <EHB 28-Jan-85>
handRest
; Get here with D0=error code, A0=result ptr. Must perserve<C169>
; them while restoring mp state from stack. D1/A1 are free.
MOVE.L D0,D1 ; <C169>
MOVE.L A0,A1 ; <C169>
MOVE.L (SP)+,A0 ; restore handle <EHB 28-Jan-85> <C169>
MOVE.B (SP)+,D0 ; <EHB 28-Jan-85> <C169>
_HSetState ; <C169>
MOVE.L D1,D0 ; restore saved results <C169>
MOVE.L A1,A0 ; <C169>
RTS ; <EHB 28-Jan-85>
PtrToXHandTrap
EXG A0,A1 ; save source pointer
MOVE.L D0,D1 ; save length
_SetHandleSize ; Set the handle length
BRA.S cloneCommon
PtrToHandTrap
MOVE.L A0,A1 ; save source pointer
MOVE.L D0,D1 ; save length
_NewHandle
; A0 contains dest. handle, A1 contains source pointer, D2 offset into dest, D1
; amount to move
cloneCommon
BNE.S noRoom ; didn't get space, so skip
MOVEQ #0,D2 ; no offset for these
clone2Common
MOVE.L A0,-(SP) ; save handle for return
MOVE.L (A0),A0 ; dereference
ADD.L D2,A0 ; add in offset (=0 most times)
EXG A0,A1 ; switch source/dest
MOVE.L D1,D0 ; restore length
_BlockMoveData ; counts on D0 being returned 0
MOVE.L (SP)+,A0 ; get handle for return
noRoom
RTS
; Concatenates handle in A0 onto handle in A1
HandAndHandTrap
_HGetState ; D0 <- mp state <C169>
MOVE.B D0,-(SP) ; save across call <C169>
MOVE.L A0,-(SP) ; save the handle
_HNoPurge ; <C169>
_GetHandleSize ; and get the size
TST.L D0 ; purged handle?
BMI.S handRest ; =>yes, exit pronto
MOVE.L D0,D1 ; save add-on length
EXG A1,A0 ; get dest handle
_GetHandleSize
MOVE.L D0,D2 ; save existing length
BMI.S handRest ; error in dest exit pronto
ADD.L D1,D0 ; add in new length
_SetHandleSize
BNE.S handRest ; escape if error
MOVE.L (A1),A1 ; dereference source
BSR clone2Common ; go do it
BRA handRest
PtrAndHandTrap
MOVE.L D0,D1 ; save add-on length
EXG A1,A0 ; get dest handle
_GetHandleSize
MOVE.L D0,D2 ; save existing length
ADD.L D1,D0 ; add in new length
_SetHandleSize
BNE.S noRoom ; escape if error
BRA.S clone2Common ; go do it
;-------------------------------------------------------------------
; Pulled from file: Method.TEXT
;
; PROCEDURE MethodDispatch ( 'uses nonstandard stack params ' );
; (SP) = selector table address
; 4(SP) = actual return address
; 8(SP) = receiver
; 07 May 85 JTC Written by MacApp group -- typed by their new AA!
; 17 Jun 86 DBG Tweaks for performance
;-------------------------------------------------------------------
EXPORT MethodDispatch
MethodDispatch
MoveA.L (SP)+,A0 ; A0 := Method table address
MoveA.L 4(SP),A1 ; A1 := receiver handle
MoveA.L (A1),A1 ; A1 := receiver ptr
Move.W (A1),D0 ; D0 := receiver's class #
Move.W (A0)+,D1 ; D1 := number of implementations of method (-1)
Cmp.W (A0),D0 ; cached class # versus receiver class #
BNE.S search ; Not Equal => must search table
jmpMeth
Move.W 2(A0),D0 ; D0 := A5/A0 relative offset to method
BClr #0,D0 ; 0=>A5; 1=>A0
BNE.S A0Rel ; 1 => do A0
Jmp 0(A5,D0.W) ; via Jump Table
A0Rel
Jmp 2(A0,D0.W) ; jump to method, A0 pointing to word before offset
search
Move.W D0,(A0) ; cache the class #
Move.L A0,D2 ; D2 := cache address
loopa
AddQ.L #4,A0 ; A0 := ptr to next class # in table
Cmp.W (A0),D0 ; next class # versus given class #
DBCC D1,loopa ; fall through if (A0) unsigned <= D0
BEq.S found ; Eq => found it
MoveA.L MASuperTab,A1 ; A1 := handle to Superclass table
MoveA.L (A1),A1 ; A1 := ptr to Superclass table
BrA.S doSuper ; Get Superclass
loopb
AddQ.L #4,A0 ; A0 := ptr to next class # in table
loop2
Cmp.W (A0),D0 ; next class # versus given class #
DBCC D1,loopb ; fall through if (A0) unsigned <= D0
BEq.S found ; Eq => found it
doSuper
Move.W 0(A1,D0.W),D0 ; D0 := Superclass # of D0 (D0 is always even!)
BNE.S loop2 ; Not Equal => still worth searching
; Error condition: method not found
MoveA.L D2,A1 ; A1 := cache address
Clr.L (A1)
Move.L MAErrProc,A1 ; address of error routine
Jmp (A1)
found
MoveA.L D2,A1 ; A1 := cache address
Move.W 2(A0),2(A1) ; store method offset in cache
BrA.S jmpMeth
;-------------------------------------------------------------------
; End of MacApp Method code...
;-------------------------------------------------------------------
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; File: Used to be . . . AdMath.ASM . . . now part of Toolbox Utilities.
;
; Assembly language FixMul, FixDiv, Sqrt, FixRatio, FracMul, FracDiv,
; and FracSqrt.
; Written by J. Coonen 8 Sep 84.
; 13 Sep 84 JTC added FixRatio, FracMul, FracDiv, and FracSqrt.
; 22 Jan 85 CRC added FixSin, removed ones in ROM, Sqrt; tweaked for Pascal
; 4 Feb 85 CRC tweaked FixSin into FracSin, added fixed point ROM sources
; 21 Apr 85 JTC Fixed up for ROM use: <18Apr85>
; 1) Remove Macro definitions.
; 2) Remove FFixMul(Fixed, Fracd) entry point -- it's the same as FracMul!
; 3) Add QD fixed-point routines to comment.
; 4) Fix bug in FixRound.
; 5) Renamed FixFixRatio (was FFixRatio)
; 22 Apr 85 JTC Modified calling convention for LongMul to be custom for Bill. <22Apr85>
; 24 Apr 85 JTC Modified all calls to preserve all but A0. <24Apr85>
; 13 May 85 JTC One last bash at new routines. <13May85>
; <C156>15 Sep 86 CRC FixRound: Add almost 1/2 instead of -1/2 in negative case
; <C576>30 Dec 86 EHB CRC LongMul,FixMul,FracMul,FixRatio were trashing too many registers
; Added a few RTD's for speed
; <C693>25 Jan 87 EHB Undid some mysterious changes in FixRatio that broke it
;
; FUNCTION FixMul (x, y: Fixed): Fixed; { returns x*y, signed }
;
; FUNCTION FracMul (x, y: Fracd): Fracd; { returns x*y }
;
; PROCEDURE LongMul (x, y: LONGINT; VAR z: Int64bit); { returns 64-bit x*y, signed }
;
; FUNCTION FixDiv (x, y: Fixed): Fixed; { returns x/y, signed }
;
; FUNCTION FracDiv(x, y: Fracd): Fixed; { returns x/y }
;
; FUNCTION FixRatio(x, y: Integer): Fixed; { returns x/y }
;
; FUNCTION FixRound (x: Fixed) : INTEGER; { returns x, rounded to integer }
;
; FUNCTION FracSqrt (x: Fracd) : Fracd; { returns square root of x }
;
; FUNCTION FracSin (x: Fixed) : Fracd; { returns Sin(x) }
;
; FUNCTION FracCos (x: Fixed) : Fracd; { returns Cos(x) }
;
; FUNCTION FixATan2 (x, y : LongInt): Fixed; { returns ATan(y/x) }
;
; FUNCTION HiWord (x: LONGINT) : INTEGER; { returns hi word of x }
;
; FUNCTION LoWord (x: LONGINT) : INTEGER; { returns lo word of x }
;
; FUNCTION Long2Fix, Fix2Long, Fix2Frac, Frac2Fix (x: inputType): outputType;
;
; FUNCTION Fix2X, X2Fix, Frac2X, X2Frac (x: inputType): outputType;
;
; Type Fixed is 32-bit binary fixed-point with binary point between
; high and low words. Sign is kept a la 2's-complement.
; Type double is 64-bit IEEE binary floating point.
; Type Fracd is 32-bit binary fixed point-point with binary point
; after leading bits. Sign is kept a la 2's-complement.
;
; Exceptional cases:
; Fixed overflow is set to $7FFFFFFF when positive, $80000000 when
; negative.
; Division by zero yields $7FFFFFFF when x is positive or zero,
; and $80000000 when x is negative.
;
; Calling conventions:
; Lisa/Mac Pascal stack arguments and return values.
; Exception: LongMul preserves all but A0 -- special for quickdraw. <22Apr85>
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; When this package is adapted for RAM, set this value to 1. It prevents
; collisions with sacred names defined in first-round system.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
FixedPRAM EQU 0 ; <28aug85> BBM
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; There are two flavors of multiply, FracMul and FixMul. FracMul uses the
; top 35 bits of the 64-bit product: the top two are shifted off the left,
; the the last bit is used for rounding. FixMul uses the middle 32 bits
; of the product, with the attendant overflow checks, and rounds with a
; 32nd bit.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; .PROC FixMath,0 Don't need this in toolbox utilities. <21Apr85>
EXPORT FracMul
EXPORT FracDiv
EXPORT FixDiv
EXPORT FracSqrt
EXPORT FracSin
EXPORT FracCos
EXPORT FixATan2
EXPORT Long2Fix
EXPORT Fix2Long
EXPORT Fix2Frac
EXPORT Frac2Fix
EXPORT Fix2X
EXPORT X2Fix
EXPORT Frac2X
EXPORT X2Frac
IF FixedPRAM THEN
EXPORT RLongMul
EXPORT RFixMul
EXPORT RHiWord
EXPORT RLoWord
EXPORT RFixRatio
EXPORT RFixRound
ELSE
EXPORT LongMul
EXPORT FixMul
EXPORT HiWord
EXPORT LoWord
EXPORT FixRatio
EXPORT FixRound
ENDIF
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; PROCEDURE LongMul (x, y: LONGINT; VAR z: Int64bit); { returns 64-bit x*y, signed }
;
; CLOBBERS ONLY A0
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
IF FixedPRAM THEN
RLongMul
ELSE
LongMul
ENDIF
; RTS EQU 8
; Z EQU 12
; Y EQU 16
; X EQU 20
MOVEM.L D0-D1,-(SP) ;save work registers
MOVE.L 16(SP),D1 ;get y
MULS.L 20(SP),D0:D1 ;multiply x by y to form 64 bit result
MOVE.L 12(SP),A0 ;get var Z
MOVE.L D0,(A0)+ ;store high word
MOVE.L D1,(A0)+ ;store low word
MOVEM.L (SP)+,D0-D1 ;restore work registers
RTD #12 ;strip params and return
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; FracMul, FixMul
;
; CLOBBERS ONLY A0
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
FracMul
LEA 3,A0 ; mark as FracMul (# of extra bits above result)
BRA.S commonMul
IF FixedPRAM THEN
RFixMul
ELSE
FixMul
ENDIF
CMP.L #$00010000,4(SP); is y 1?
BEQ.S returnX
CMP.L #$00010000,8(SP); is x 1?
BEQ.S returnY
LEA 17,A0 ; mark as FixMul (# of extra bits above result)
commonMul
RET EQU 16 ; return address (after 4 regs)
Y EQU RET+4 ; Y parameter
X EQU Y+4 ; X parameter
RESULT EQU X+4
MOVEM.L D0-D2/A1,-(SP) ; save everything but A0
MOVE.L Y(SP),D1 ; get argument y
SMI D2 ; remember sign
TST.L X(SP) ; check sign of x
SMI D0 ; remember its sign as well
EOR.B D0,D2 ; combine to signs together
EXTB.L D2 ; make it a mask for overflow check
MULS.L X(SP),D0:D1 ; get argument x; multiply by y
MOVE.L D1,-(SP) ; save 64 bit result away for bit extract
MOVE.L D0,-(SP)
; overflow occured if top bits are not equal to xored signs
MOVE.L A0,D0 ; 16 for FixMul; 2 for FracMul
BFEXTS (SP){0:D0},D1 ;get either first 3 or first 17 bits
CMP D1,D2
BEQ.S @noOverFlow
; if one of the operands are 0, and the other one is negative, weÕll get here even though
; there is no overflow. Check for 0 in result going on.
MOVE.L (SP)+,D1 ;get high word of result
OR.L (SP)+,D1 ;zero if and only if the low and high words are zero.
BEQ.S @returnResult
MOVEQ #-1,D1 ;-1
LSR.L #1,D1 ;$7FFFFFFF
EOR.L D2,D1 ;$7FFFFFFF (largest positive) or $80000000 (largest negative)
BRA.S @returnResult
@noOverFlow
;no overflow; extract result
SUBQ #1,D0 ;get sign bit as well
BFEXTS (SP){D0:0},D1 ;get 32 bits of results (0 = 32: assembler bug/oversight)
;if 1/2 bit is set, add 1. Note that to be painstakingly correct, if the result is negative
;add 1 only if a bit smaller than the 1/2 bit is also set. The exact one-half case should
;not round up.
ADD #32,D0 ; bump D0 to 1/2 bit
BFEXTU (SP){D0:1},D2 ; get the 1/2 bit
BEQ.S @commonEnd
TST.L D1 ; result is minus?
BPL.S @add1
ADDQ #1,D0 ; advance to next bit (the 1/4 bit)
MOVEQ #64,D2 ;
SUB D0,D2 ; determine number of bits remaining
BFEXTU (SP){D0:D2},D0
BEQ.S @commonEnd
@add1
ADDQ.L #1,D1 ; bump the result
@commonEnd
ADDQ #8,SP ; throw away 64 bit result
@returnResult
MOVE.L D1,RESULT(SP) ; save result
MOVEM.L (SP)+,D0-D2/A1 ; restore registers
RTD #8 ; strip params and return
returnX
MOVE.L 8(SP),12(SP)
RTD #8
returnY
MOVE.L 4(SP),12(SP)
RTD #8
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Restore sign to D0, with check for overflow. On overflow store max
; value with appropriate sign.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
reSign
TST.L D0
BMI.S fixOver ; result must be 80000000
TST.B D6
BEQ.S TwoParmExit
NEG.L D0
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Common exit routine for all two parm routines.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
TwoParmExit
MOVE.W #8,8(A6) ; A6: savedA6 << RET << x ...
MOVE.L D0,16(A6) ; A6: savedA6 << RET << x << y << result slot
BRA.S CustomExit
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Common exit routine for all one parm routines.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
OneParmExit
MOVE.W #4,8(A6) ; A6: savedA6 << RET << x ...
MOVE.L D0,12(A6) ; A6: savedA6 << RET << x << result slot
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Custom exit -- expect 8(A6) to be amount to kill from stack
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
CustomExit
MOVEM.L (SP)+,D0-D6/A1 ; restore registers
UNLK A6
MOVE.L (SP)+,A0
ADDA.W (SP),SP ; kill the params
JMP (A0)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Common entry routine for all.
; Preserves all but A0.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
StdEntry
MOVE.L (SP)+,A0 ; local return address
LINK A6,#0
MOVEM.L D0-D6/A1,-(SP) ; save scratch registers
JMP (A0) ; return
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Common startup routine fetches x,y from 12(A6) and unpacks into D1,D2.
; Sign of result is stored in bit #15 of D6.16.
; NOTE: D1 and D2 are reversed from the Adobe version of these routines
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
fixArgs
MOVEM.L 8(A6),D1-D2 ; D1=y D2=x
fixArg1
TST.L D1
SMI D6
BPL.S @41
NEG.L D1
@41
TST.L D2
BPL.S @43
NEG.L D2
NOT.B D6 ; bit 7 is XOR of x,y signs
@43
RTS
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Forces max value with correct sign.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
fixOver
MOVEQ #1,D0
ROR.L #1,D0 ; get max negative Fixed, $80000000
TST.B D6
BNE.S TwoParmExit
SUBQ.L #1,D0 ; 7FFFFFFF when positive
BRA.S TwoParmExit
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; FixDiv:
; Dividing xxxx.xxxx by yyyy.yyyy. Must prenormalize y to run division
; algorithm. To minimize number of divide steps, prenormalize x as well.
; Step count = 1-int + 16-frac + 1-round + y-shifts - x-shifts - 1-DBRA.
; Cases: count <= 0 quo := 0
; 0 < count < 32 quo := as computed
; count >= 32 quo := fixOver
; Note that we can accommodate the "extra" round bit because the signed
; result is really only 31 bits wide in magnitude.
;
; FracDiv:
; Step count = 1-int + 30-frac + 1-round + y-shifts - x-shifts - 1-DBRA.
;
; FixDiv:
; Step count = 1-int + 16-frac + 1-round + y-shifts - x-shifts - 1-DBRA.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
FracDiv
BSR.S StdEntry
MOVEQ #31,D3 ; 1 + 30 + 1 - 1 = signature of FixRatio
BRA.S comDiv
FixDiv
BSR.S StdEntry
MOVEQ #17,D3 ; 1 + 16 + 1 - 1 = signature of ...
comDiv
BSR.S fixArgs
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Initialize quo, have step count in D3; and check for division by zero.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
MOVEQ #0,D0 ; initialize quo
TST.L D1
BNE.S @13 ; entry to next loop, D1 tested
BRA.S FixOver
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Loop to prenormalize y.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@11
ADDQ.W #1,D3
ADD.L D1,D1
@13
BPL.S @11
TST.L D2
BEQ.S TwoParmExit ; hasty retreat if 0/0
@14 BRA.S @17 ; entry to next loop, D2 tested
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Loop to prenormalize x.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@15
SUBQ.W #1,D3
ADD.L D2,D2
@17
BPL.S @15
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Check for cases above, based on step count in D3.W
; The 0-based quotient bit count is in D3, for a DBRA loop below.
; D3 <= 0 means that there are no (nonzero) quotient bits to compute,
; that is, the result is zero. D3 < 32 means that we're computing
; at most 32 real bits, so there can be no overflow.
; Now the subtle part: with normalized dividend and divisor, there is at
; most one leading 0 bit before the nonzero quotient begins. That means
; that when the D3 = 32 (that is, 33 quotients bits coming), we overflow
; precisely when the leading quotient bit is 1; otherwise, we just fall
; into the divide loop where a zero quotient bit would have taken us.
; Finally D3 > 32 gurantees overflow.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
TST.W D3
BLE.S TwoParmExit ; StdExit, 0 is the result
CMPI.W #32,D3 ; changed for #31 to # 32 <A279/28Oct86>
BLT.S L23 ; fall into loop, guaranteed no overflow <A343/03Nov86>
BGT.S fixover ; was bra.s until now, overflow guaranteed <A343/03Nov86>
CMP.L D1,D2 ; D1 < D2 --> CarrySet -->first bit is zero <A343/03Nov86>
BCS.S L27 ; falls in when 0 quo bits go <A343/03Nov86>
BRA.S fixOver
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Divide loop, to divide D2 by D1, developing D3.W quotient bits into D0.
; At each step quotient is left shifted one place; in event of carry-out
; be sure to force subtract. Because of tests above, there's no chance
; of overflow except during round step.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
L21
ADD.L D0,D0 ; make way for next quo bit
;;; BCS.S FixOver ; remove test from inner loop <A279/27Oct86>
ADD.L D2,D2 ; shift dividend
BCS.S L25 ; force subtract on carry
L23
CMP.L D1,D2 ; divisor vs dividend
BCS.S L27 ; skip subtract if too small
L25
SUB.L D1,D2
ADDQ.W #1,D0 ; no carry here
L27
DBRA D3,L21
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Use the low bit of D0 to round the result.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
LSR.L #1,D0
BCC.S reSign
ADDQ.L #1,D0
BRA.S reSign
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Square root of a Frac xx.xxxxxxxx . In this case, the leading two
; bits of the Fract are BOTH taken to be integer, that is, the value is
; interpreted as unsigned.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Square roots based on classical schoolboy algorithm.
; P = (SUM Aj*10^-j)^2
; = A1 * A1 * 10^-2 +
; ( 2(10*A1) + A2 ) * A2 * 10^-4 +
; ( 2(10^2*A1 + 10*A2) + A3 ) * A3 * 10^-6 +
; ( 2(10^3*A1 + 10^2*A2 + 10*A3) + A4 ) * A4 * 10^-8 + ...
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
FracSqrt
BSR.S StdEntry
MOVE.L 8(A6),D3 ; fetch input Frac
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Know that lead bit of root is 0, so only 31 bits plus a round bit are
; required. Alas, this just spills over a longword, so compute in a
; 64-bit field. Compute root into D0-D1. Maintain radicand in D2-D3.
; Loop counter in D4. Before each step, the root has the form:
; <current root>01 and after each step: <new root>1, where the number
; shown spans D0 and the highest two bits of D1.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
MOVEQ #0,D0
MOVEQ #1,D1
ROR.L #2,D1 ; D1 := 4000 0000
MOVEQ #0,D2 ; clear high radicand
MOVEQ #31,D4 ; need 32 bits less 1-DBRA
frSqrtLoop
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Try radicand minus trial root. Use subtle fact that C is the complement
; of the next root bit at each step.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
SUB.L D1,D3
SUBX.L D0,D2 ; no carry means root=1
BCC.S @72
ADD.L D1,D3
ADDX.L D0,D2
@72
DC.W $0A3C ;EORI #16,CCR - complement X bit
DC.W $0010
ADDX.L D0,D0 ; set root bit while shifting
ADD.L D3,D3 ; shift radicand two places
ADDX.L D2,D2
ADD.L D3,D3
ADDX.L D2,D2
DBRA D4,frSqrtLoop
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Shift the 32-bit root in D0 right one bit and round.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
LSR.L #1,D0
BCC.S OneParmExit
ADDQ.L #1,D0
BRA.S OneParmExit ; <23Apr85>
; Experiment in crunching: FixRatio written using common code, at what cost?
IF FixedPRAM THEN
RFixRatio
ELSE
FixRatio
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; FixRatio(numerator,denominator: INTEGER): Fixed;
;
; CLOBBERS ONLY D0-D1
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
ENDIF
MOVE 4(SP),D0 ; get denominator
BEQ.S @overFlow ; check for division by zero
MOVEQ #0,D1 ; clear high part of D1
MOVE 6(SP),D1 ; get numerator
CMP D0,D1
BEQ.S @returnOne
EXT.L D0
SWAP D1 ; multiply denominator by $1000
DIVS.L D0,D1 ; all done
MOVE.L D1,8(SP) ; return fixed result
RTD #4 ; strip params and return
@overFlow
MOVEQ #-1,D1
LSR.L #1,D1 ; a very large positive number
TST 6(SP) ; is numerator negative?
BPL.S @0
NEG.L D1 ; a very large negative number
@0 MOVE.L D1,8(SP) ; return fixed result
RTD #4 ; strip params and return
@returnOne
MOVEQ #1,D1
SWAP D1
MOVE.L D1,8(SP) ; return fixed result
RTD #4 ; strip params and return
chkSign TST.B D6 ; was original signed?
BEQ.S @9 ; common code for this & FracSin, FracCos
NEG.L D0
@9 BRA.S OneParmExit
FixRatEasy
MOVEQ #1,D0 ; 0000.0001 <23Apr85>
SWAP D0 ; make it 1.0 <23Apr85>
BRA.S OneParmExit
IF FixedPRAM THEN
RLoWord
ELSE
LOWORD
ENDIF
;----------------------------------------------------
;
; FUNCTION LoWord(x: Fixed): INTEGER;
;
MOVE.W 6(SP),8(SP) ;GET LO WORD
BRA.S StripRet
;----------------------------------------------------
;
; FUNCTION HiWord(x: Fixed): INTEGER;
;
IF FixedPRAM THEN
RHiWord
ELSE
HIWORD
ENDIF
MOVE.W 4(SP),8(SP) ;RETURN HI WORD OF RESULT
StripRet MOVE.L (SP)+,(SP) ;STRIP PARAM
RTS ;RETURN
;----------------------------------------------------
;
; FUNCTION FixRound(x: Fixed): INTEGER;
;
; Tricky routine requires that one add 1/2 to the MAGNITUDE of x, then CHOP toward 0.
; Chopping a 2's-complement value requires an increment if the value of the fraction is
; nonzero. To be polite, also check for overflow:
; $7FFF8000 and above carries out to $8000xxxx, which must be pinned at $7FFF.
; $80007FFF and above (in magnitude) carry out to $7FFF8xxx, which must be pinned at $8000.
; Lovely trick: note that regardless of its negation, the low word of D1 is $8000! Use it!
; Subtle case: it looks simple to add 1/2 (toward +INF) and take floor (toward -INF) to get FixRound
; to come out. Alas, this messes up in half-way cases, to wit, 3/2 --> 2 but -3/2 --> -1 !!!
; change made 15-Sep-86 CRC: add almost 1/2 instead of -1/2 in negative case
IF FixedPRAM THEN
RFixRound
ELSE
FIXROUND
ENDIF
MOVE.L (SP)+,A0 ;get return address
MOVEQ #1,D1
ROR.W #1,D1 ;compute $00008000
MOVE.L (SP)+,D0 ;get passed argument
BPL.S @positive
NOT D1 ;for negative, make it $00007FFF
@positive ADD.L D1,D0 ;round up, but not as far if negative
BVC.S @notTooBig ;fell off the end of the positive world
MOVEQ #-2,D0 ;get $FFFFFFFE
ROR.L #1,D0 ;compute $7FFFFFFF
@notTooBig
SWAP D0 ;get hi word result
MOVE D0,(SP) ;and return integer
JMP (A0) ;go home
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;
; FUNCTION FracSin (x: Fixed) : Fract; { returns Sin(x) }
;
; FUNCTION FracCos (x: Fixed) : Fract; { returns Cos(x) }
;
; Written by KLH 8 May 85
;
; Description: Fixed Point Sine & Cosine. It would be wise to use values
; of PI/4, PI/2 or PI obtained from FixATan2 for angle conversions.
; Undone: 1) code would be improved if A2 were saved and restored in
; standard entry and exits.
; 2) Need to make standard bypass when reduced arguments are 0, maybe.
;
;
; (|x| div Pi/4) mod 8 Argument Range sin (x) cos (x)
; D6 := |x| div Pi/4 D3 := x
;
; 0 0 to Pi/4 sin (x) cos (x)
; 1 Pi/4 to Pi/2 cos (Pi/2 - x) sin (Pi/2 - x)
; 2 Pi/2 to 3*Pi/4 cos (x) -sin (x)
; 3 3*Pi/4 to Pi sin (Pi/2 - x) -cos (Pi/2 - x)
; 4 Pi to 5*Pi/4 -sin (x) -cos (x)
; 5 5*Pi/4 to 3*Pi/2 -cos (Pi/2 - x) -sin (Pi/2 - x)
; 6 3*Pi/2 to 7*Pi/4 -cos (x) sin (x)
; 7 7*Pi/4 to 2*Pi -sin (Pi/2 - x) cos (Pi/2 - x)
;
; Note; 1) when D6 is odd D3 := Pi/2 - D3
; 2) if (cosine entry) then D6 := D6 + 2, use sine column
; 3) if (x < 0) and (sine entry) then D6 := D6 + 4
; 4) 'move.b #$66,-(sp)'
; 'btst D6,(sp)+' tests (D6 mod 8) bit of $66
; 5) the above scheme reduces all cosine and sine calls to
; the appropriate sine or cosine in the range 0 to Pi/4
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
FracCos
BSR.S StdEntry
MOVEQ #2,D6 ;This is a Cosine, PI/2 phase shift
BRA.S FSin2
FracSin
BSR.S StdEntry
MOVEQ #0,D6 ;flag that this is a Sine routine, No phase shift
FSin2
MOVE.L 8(A6),D3 ;get angle
bpl.s @3 ;input argument is postive
tst.l D6
bne.s @2 ;not Sine routine
addq #4,D6 ;Add PI phase shift, argument negative for sine
@2 neg.l D3
@3 move.l #$0000c910,D5 ;D5 := PI/4 (fixed)
divu D5,D3
add.l D3,D6
clr.w D3
swap D3
btst #0,D6
beq.s @4
sub.w D5,D3 ; D3 := D3 - PI/4
neg.w D3 ; D3 := -D3
@4 swap D3 ; frac := fixed/2
lsr.l #3,D3
MOVE.l A2,-(SP) ;need an address register
SUB.L #16,SP ;space for 4 FracMul's function result
move.l D3,-(sp)
move.l D3,-(sp)
bsr FracMul ;d5 := sqr (D3)
MOVE.L (SP)+,D5
move.b #$66,-(sp)
btst D6,(sp)+
bne.S PolyCos
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;
; sin (x) := (x/2)*(sn0 + x2*(sn1 + x2*sn2)), where x2 := sqr (x/2)
;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
LEA sn0,A2 ;polynomial constants Sine
MOVEQ #4,D4 ;2 iterations, counting from 0 by fours.
bra.s PolyLoop
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;
; cos (x) := cs0 + x2*(cs1 + x2*(cs2 + x2*cs3)), where x2 := sqr (x/2)
;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
PolyCos LEA cs0,A2 ;polynomial constants for Cosine
MOVEQ #8,D4 ;3 iterations, counting from 0 by fours.
PolyLoop
move.L 4(A2,D4),-(sp)
@3 MOVE.l D5,-(SP) ;push sqr (x) onto stack
bsr FracMul
move.L 0(A2,D4),D0
add.L D0,(sp) ;add coefficient to stack
SUBQ #4,D4
BPL.S @3
move.b #$66,-(sp)
btst D6,(sp)+
bne.S NotSine
move.l d3,-(sp) ;push original argument onto stack
jsr FracMul ;do final multiply for Sine
NotSine
move.l (sp)+,D0 ;pop result into D0 register
MOVE.L (SP)+,A2 ;restore extra register
move.b #$f0,-(sp)
btst D6,(sp)+
beq.s @9
neg.l D0
@9 Bra.S OneParmExit
sn0 DC.L $7FFFD609 ; 1.9999899949540321990 0.000000561
sn1 DC.L $AAB3314D ; -1.3328129532011865770 0.000000561
sn2 DC.L $10A208E5 ; 0.2598898155860768873 0.000000561
cs0 DC.L $40000000 ; 1.0
cs1 DC.L $800011A7 ; -1.9999957911835540090 0.000000032
cs2 DC.L $2AA7F29A ; 0.6665007113846229170 0.000000032
cs3 DC.L $FA6E2A42 ; -0.0870260574471380774 0.000000032
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;
; FUNCTION FixATan2 (x, y: LONGINT): Fixed; { returns ArcTan (x, y) }
;
; Written by KLH 8 May 85
;
; Description: FixATan2 returns the angle (fixed, radians) in the range
; [-PI to PI] to the point (x, y: Longint). For consistency with fracCos
; and fracSin it would be wise to use value of PI/4, PI/2 or PI obtained
; from this function for angle conversions.
; Undone: 1) (0, 0) currently yields 0, is this OK?
; 2) code would be improved if A2 were saved and restored in
; standard entry and exits.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
FixATan2
BSR.S StdEntry
moveq #0,D6
MOVE.L 12(A6),D3 ; get X
bpl.s @1 ; if X < 0 then
addq #2,D6 ; set 2nd bit of D6
neg.l D3 ; X := abs |X|
bpl.s @1
subq.l #1,D3 ; uh oh, it's still negative, make largest positive <fixed> <5>
@1 MOVE.L 8(A6),D0 ; get Y
bpl.s @2 ; if Y < 0s then
addq #1,D6 ; set lowest bit of D6
neg.l D0 ; y := |y|
bpl.s @2
subq.l #1,D0 ; make largest positive <fixed> <5>
@2 MOVE.l A2,-(SP) ; need an address register
SUB.L #32,SP ; space for 8 Longints function results 8LP
cmp.l D3,D0 ; D0 - D3
ble.s bigger ; is |Y| > |X| if yes then
addq #4,D6 ; set 3rd bit of D6
move.l D3,-(sp) ; argument for ArcTan is |X|/|Y|
beq.s NoPoly ; reduced argument is zero
move.l D0,-(sp)
bra.s GetATanArg
NoPoly move.l D3,D0
NoPoly2 Add.l #36,sp ; clean up stack 0LP
bra.s bypass
bigger move.l D0,-(sp) ; reduced argument for ArcTan is |Y|/|X|
beq.s NoPoly2 ; reduced argument is zero or 0/0
move.l D3,-(sp)
GetATanArg ; 10LP
bsr FracDiv
MOVE.L (SP),D3 ;save argument
move.l (sp),-(sp) ; 9LP
bsr FracMul ;D5 := sqr (D3)
MOVE.L (SP)+,D5 ; 6LP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;
; ArcTan (x) := x*(at0 + x2*(at1 + x2*(at2 + x2*(at3 + x2*(at3 + x2*at5))))),
;
; where x2 := sqr (x)
;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
LEA at0,A2 ; polynomial constants for ArcTangent 6LP
MOVE.L 20(a2),-(sp) ; push last coefficient onto stack 7LP
MOVEQ #16,D4 ; 5 iterations, counting from 0 by fours.
@3 MOVE.l D5,-(SP) ; push sqr (x) onto stack
bsr FracMul
move.L 0(A2,D4),D0
add.L D0,(sp) ; add coefficient to stack
SUBQ #4,D4
BPL.S @3
; 2LP
move.l d3,-(sp) ; push original argument onto stack
jsr FracMul ;do final multiply
move.l (sp)+,D0 ; pop result into D0 register
MOVEQ #14,D2 ; with ArcTangent
LSR.L D2,D0 ; shift right 14 bits, for frac to fixed
bcc.s bypass
addq.l #1,D0 ; round up
bypass MOVE.L (SP)+,A2 ; restore extra register
move.l #$00019220,D5 ; D5 := PI/2 (fixed)
btst #2,D6
beq.s @2 ; X < Y
sub.l D5,D0 ; D0 := D0 - PI/2
neg.l D0 ; D0 := -D0
@2 btst #1,D6
beq.s @1 ; X was positive
lsl.l #1,D5 ; D5 := PI
sub.l D5,D0 ; D0 := D0 - PI
neg.l D0 ; D0 := -D0
@1 btst #0,D6
beq.s @0 ; Y was positive
neg.l D0 ; D0 := -D0
@0 Bra.S TwoParmExit
at0 DC.L $3FFFA073 ; 0.9999772190799163233 0.000001662
at1 DC.L $EAB64EBE ; -0.3326228278407496104 0.000001662
at2 DC.L $0C62F72C ; 0.1935403757729599042 0.000001662
at3 DC.L $F88C77F2 ; -0.1164264811847172587 0.000001662
at4 DC.L $035E92FE ; 0.0526473506160217409 0.000001662
at5 DC.L $FF3FFE62 ; -0.0117191354060452945 0.000001662
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;
; FUNCTION Fix2X (x: Fixed ): Extended;
; FUNCTION Frac2X (x: Fract ): Extended;
;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
Fix2X
move.w #$400E,D1 ; set extended exponent for 2^15
bra.s ComE
Frac2X
move.w #$4000,D1 ; set extended exponent for 2^1
ComE MOVE.L (SP)+,A0 ; save return address
move.l (sp)+,D0 ; put Fixed or Frac into D0
bne.s NotZero
moveq #0,D1 ; zero exponent
bra.s fin
NotZero bpl.s shftgn
add.w #$8000,D1 ; set Extended sign bit
neg.l D0
bmi.s fin ; largest negative number, thus it is normalized
shftgn subq.w #1,D1 ; decrement Extended exponent
lsl.l #1,D0 ; shift until normalized
bpl.s shftgn
fin move.l (sp),A1 ; get effective address of return argument
move.w D1,(A1) ; stuff sign & exponent
move.l D0,2(A1) ; stuff significand
clr.l 6(A1) ; clear low word of Extended
jmp (A0)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;
; FUNCTION X2Fix (x: Extended ): Fixed;
; FUNCTION X2Frac(x: Extended ): Fract;
;
; Note: Assumes Extended numbers are normalized
;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
X2Fix
move.w #$400e,D1 ; exponent for Ext. for correct Fixed significand
bra.s X2F
X2Frac
move.w #$4000,D1 ; exponent for Ext. for correct Frac significand
X2F MOVEm.L (SP)+,A0/A1 ; save return address/get Extended address
move.w (A1),D0 ; get exponent
bclr #15,D0 ; D0 := abs (D0)
sub.w D0,D1 ; D1 := D1 - D0
blt.s MaxIt ; either a NaN, Inf or too large for fixed or frac
move.l 2(A1),D0 ; get most significant part of significand
tst.w D1
bne.s @1 ; unnormalize number
tst 6(A1) ; is the 33rd bit set necessitating a round up
bra.s @2
@1 cmp.w #32,D1 ; D1 - 32
blt.s @3 ; Ok to Shift
bne.s ZeroIt ; even MSB shifted too far to cause a rounding
moveq #0,D0 ; 32 bit shift, zero leading 32 bits & check 33rd
tst 2(A1) ; is the 33rd bit set necessitating a round up
@2 bmi.s RndUp
bra.s rtnX2F
@3 lsr.l D1,D0 ; shift
bcc.s rtnX2F
RndUp addq.l #1,D0 ; round up
bcs.s MaxIt ; MaxIt if overflow
rtnX2F tst (A1)
bmi.s NegRslt
tst.l D0
bmi.s MaxIt ; positive value too large
FinX2F move.l D0,(sp)
jmp (A0)
ZeroIt moveq #0,D0 ; put here to save a word
NegRslt neg.l D0
ble.s FinX2F ; D0 was zero or a valid negative value
MaxIt tst.w (A1)
MaxE2 bpl.s @1
moveq #1,D0 ; move.l $00000001,D0 -> $80000000,D0
bra.s @2
@1 clr.l D0
subq.l #2,D0 ; move.l $fffffffe,D0 -> $7fffffff,D0
@2 ror.l #1,D0
bra.s FinX2F
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;
; FUNCTION Long2Fix (x: Longint ): Fixed;
; FUNCTION Fix2Long (x: Fixed ): Longint;
; FUNCTION Fix2Frac (x: Fixed ): Fract;
; FUNCTION Frac2Fix (x: Fract ): Fixed;
;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
Fix2Long
moveq #16,D1
bra.s ComFF
Frac2Fix
moveq #14,D1
ComFF MOVE.L (SP)+,A0 ; save return address
move.l (sp)+,D0 ; put Fixed or Frac into D0
bpl.s @2
neg.l D0
lsr.l D1,D0
bcc.s @1
addq.l #1,D0 ; <A279/27Oct86>
@1 neg.l D0
bra.s FinX2F
@2 lsr.l D1,D0
bcc.s FinX2F
addq.l #1,D0 ; <A279/27Oct86>
bra.s FinX2F
Long2Fix
moveq #16,D1
bra.s ComLF
Fix2Frac
moveq #14,D1
ComLF MOVE.L (SP)+,A0 ; save return address
move.l (sp)+,(sp)
move.l (sp),D0 ; put Longint or Fixed into D0
asl.l D1,D0
; check for overflow & take appropriate action depending on the sign
bvc.s FinX2F ; no overflow
move.l (sp),D1 ; sets N condition code
bra.s MaxE2
END
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